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The effective magnetic anisotropy (K-eff) of nanocrystalline Fe89Zr7B4 soft magnetic alloys with different bce Fe grain sizes; (D) has been investigated by using the law of approach to saturation. The effective magnetic anisotropy of the alloys is found to be considerably depressed. The values of K-eff for the alloys (from 879 to 1038 J/m(3)) are very close to those of the nanocrystalline Fe73.5Cu1Nb3Si13.5B9 soft magnetic alloys, suggesting that the relatively lower permeability of the alloys is independent of the factor of K-eff. With an increase of grain size, K-eff is slightly increased. However, the grain size dependence of K-eff is obviously deviated from the K(eff)proportional to D-6 law, which might be mainly attributed to the residual amorphous phase in the alloys. (C) 1996 American Institute of Physics.